Abstract

In this paper we characterize the polarimetric properties of a liquid crystal on silicon display (LCoS), including depolarization and diattenuation which are usually not considered when applying the LCoS in diffractive or adaptive optics. On one hand, we have found that the LCoS generates a certain degree (that can be larger than a 10%) of depolarized light, which depends on the addressed gray level and on the incident state of polarization (SOP), and can not be ignored in the above mentioned applications. The main origin of the depolarized light is related with temporal fluctuations of the SOP of the light reflected by the LCoS. The Mueller matrix of the LCoS is measured as a function of the gray level, which enables for a numerical optimization of the intensity modulation configurations. In particular we look for maximum intensity contrast modulation or for constant intensity modulation. By means of a heuristic approach we show that, using elliptically polarized light, amplitude-mostly or phase-mostly modulation can be obtained at a wavelength of 633 nm.

© 2008 Optical Society of America

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References

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    [CrossRef]
  36. I. Moreno, C. Iemmi, A. Márquez, J. Campos, and M. J. Yzuel, "Modulation light efficiency of diffractive lenses displayed onto a restricted phase-mostly modulation display," Appl. Opt. 43, 6278-6284 (2004).
    [CrossRef] [PubMed]

2006

Q. Mu, Z. Cao, L. Hu, D. Li, and L. Xuan, "Adaptive optics imaging system based on a high resolution liquid crystal on silicon device," Opt. Express 14, 8013-8018 (2006).
[CrossRef] [PubMed]

J. Kacperski and M. Kujawinska, "Active, LCoS based laser interferometer for microelements studies," Opt. Express 14, 9664-9678 (2006).
[CrossRef] [PubMed]

V. Durán, J. Lancis, E. Tajahuerce, and Z. Jaroszewicz, "Equivalent retarder-rotator approach to on-state twisted nematic liquid crystal displays," J. Appl. Phys. 99, 113101-113106 (2006).
[CrossRef]

J. E. Wolfe and R. A. Chipman, "Polarimetric characterization of liquid-crystal-on-silicon panels," Appl.Opt. 45, 1688-1703 (2006).
[CrossRef] [PubMed]

A. Márquez, I. Moreno, J. Campos and M. J. Yzuel, "Analysis of Fabry-Perot interference effects on the modulation properties of liquid crystal displays," Opt. Commun. 265, 84-94 (2006).
[CrossRef]

D. Engström, G. Milewski, J. Bengtsson, and S. Galt, "Diffraction-based determination of the phase modulation for general spatial light modulators," Appl. Opt. 45, 7195-7204 (2006).
[CrossRef] [PubMed]

2005

Q. Wang and S. He, "A new effective model for the director distribution of a twisted nematic liquid crystal cell," J. Opt. A, Pure Appl. Opt. 7, 438-444 (2005).
[CrossRef]

A. Márquez, C. Iemmi, J. Campos, J. C. Escalera, and M. J. Yzuel, "Programmable apodizer to compensate chromatic aberrations effects using a liquid crystal spatial light modulator," Opt. Express 13, 716-730 (2005).
[CrossRef] [PubMed]

W. Osten, C. Kohler, and J. Liesener, "Evaluation and application of spatial light modulators for optical metrology," Opt. Pura Apl. 38, 71-81 (2005).

2004

Y. Lee, J. Gourlay, W. J. Hossack, I. Underwood, and A. J. Walton, "Multi-phase modulation for nematic liquid crystal on silicon backplane spatial light modulators using pulse-width modulation driving scheme," Opt. Commun. 236, 313-322 (2004).
[CrossRef]

H. Dai, K. Xu, Y. Liu, X. Wang and J. Liu, "Characteristics of LCoS Phase-only spatial light modulator and its applications," Opt. Commun. 238, 269-276 (2004).
[CrossRef]

I. Moreno, C. Iemmi, A. Márquez, J. Campos, and M. J. Yzuel, "Modulation light efficiency of diffractive lenses displayed onto a restricted phase-mostly modulation display," Appl. Opt. 43, 6278-6284 (2004).
[CrossRef] [PubMed]

2003

K. P. Proll, J. M. Nivet, K. Körner, and H. J. Tiziani, "Microscopic three-dimensional topometry with ferroelectric liquid-crystal-on-silicon displays," Appl. Opt. 42, 1773-1778 (2003).
[CrossRef] [PubMed]

I. Moreno, P. Velásquez, C. R. Fernández-Pousa, M. M. Sánchez-López, and F. Mateos, "Jones matrix method for predicting and optimizing the optical modulation properties of a liquid-crystal display," J. Appl. Phys. 94, 3697-3702 (2003).
[CrossRef]

R. Tudela, E. Martín-Badosa, I. Labastida, S. Vallmitjana, I. Juvells, and A. Carnicer, "Full complex Fresnel holograms displayed on liquid crystal devices," J. Opt. A, Pure Appl. Opt. 5, S189-S194 (2003).
[CrossRef]

2002

2001

A. Márquez, C. Iemmi, I. Moreno, J. A. Davis, J. Campos, and M. J. Yzuel, "Quantitative prediction of the modulation behavior of twisted nematic liquid crystal displays based on a simple physical model," Opt. Eng. 40, 2558-2564 (2001).
[CrossRef]

2000

A. Márquez, J. Campos, M. J. Yzuel, I. Moreno, J. A. Davis, C. Iemmi, A. Moreno, and A. Robert, "Characterization of edge effects in twisted nematic liquid crystal displays," Opt. Eng. 39, 3301-3307 (2000).
[CrossRef]

1999

S. Stallinga, "Equivalent retarder approach to reflective liquid crystal displays," J. Appl. Phys. 86, 4756-4766 (1999)
[CrossRef]

1998

1996

1995

1994

1993

1990

K. Lu and B. E. A. Saleh, "Theory and design of the liquid crystal TV as an optical spatial phase modulator," Opt. Eng. 29, 240-246 (1990).
[CrossRef]

1985

Appl. Opt.

Appl.Opt.

J. E. Wolfe and R. A. Chipman, "Polarimetric characterization of liquid-crystal-on-silicon panels," Appl.Opt. 45, 1688-1703 (2006).
[CrossRef] [PubMed]

J. Appl. Phys.

S. Stallinga, "Equivalent retarder approach to reflective liquid crystal displays," J. Appl. Phys. 86, 4756-4766 (1999)
[CrossRef]

I. Moreno, P. Velásquez, C. R. Fernández-Pousa, M. M. Sánchez-López, and F. Mateos, "Jones matrix method for predicting and optimizing the optical modulation properties of a liquid-crystal display," J. Appl. Phys. 94, 3697-3702 (2003).
[CrossRef]

V. Durán, J. Lancis, E. Tajahuerce, and Z. Jaroszewicz, "Equivalent retarder-rotator approach to on-state twisted nematic liquid crystal displays," J. Appl. Phys. 99, 113101-113106 (2006).
[CrossRef]

J. Opt. A, Pure Appl. Opt.

Q. Wang and S. He, "A new effective model for the director distribution of a twisted nematic liquid crystal cell," J. Opt. A, Pure Appl. Opt. 7, 438-444 (2005).
[CrossRef]

R. Tudela, E. Martín-Badosa, I. Labastida, S. Vallmitjana, I. Juvells, and A. Carnicer, "Full complex Fresnel holograms displayed on liquid crystal devices," J. Opt. A, Pure Appl. Opt. 5, S189-S194 (2003).
[CrossRef]

J. Opt. Soc. Am. A

Jpn. J. Appl. Phys.

I. Moreno, J. Campos, C. Gorecki, and M. J. Yzuel, "Effects of amplitude and phase mismatching errors in the generation of a kinoform for pattern recognition," Jpn. J. Appl. Phys. 34, 6423-6434 (1995).
[CrossRef]

Opt. Commun.

A. Márquez, I. Moreno, J. Campos and M. J. Yzuel, "Analysis of Fabry-Perot interference effects on the modulation properties of liquid crystal displays," Opt. Commun. 265, 84-94 (2006).
[CrossRef]

H. Dai, K. Xu, Y. Liu, X. Wang and J. Liu, "Characteristics of LCoS Phase-only spatial light modulator and its applications," Opt. Commun. 238, 269-276 (2004).
[CrossRef]

Y. Lee, J. Gourlay, W. J. Hossack, I. Underwood, and A. J. Walton, "Multi-phase modulation for nematic liquid crystal on silicon backplane spatial light modulators using pulse-width modulation driving scheme," Opt. Commun. 236, 313-322 (2004).
[CrossRef]

Opt. Eng.

A. Márquez, C. Iemmi, I. Moreno, J. A. Davis, J. Campos, and M. J. Yzuel, "Quantitative prediction of the modulation behavior of twisted nematic liquid crystal displays based on a simple physical model," Opt. Eng. 40, 2558-2564 (2001).
[CrossRef]

K. Lu and B. E. A. Saleh, "Theory and design of the liquid crystal TV as an optical spatial phase modulator," Opt. Eng. 29, 240-246 (1990).
[CrossRef]

A. Márquez, J. Campos, M. J. Yzuel, I. Moreno, J. A. Davis, C. Iemmi, A. Moreno, and A. Robert, "Characterization of edge effects in twisted nematic liquid crystal displays," Opt. Eng. 39, 3301-3307 (2000).
[CrossRef]

Opt. Express

Opt. Lett.

Opt. Pura Apl.

W. Osten, C. Kohler, and J. Liesener, "Evaluation and application of spatial light modulators for optical metrology," Opt. Pura Apl. 38, 71-81 (2005).

Other

S. T. Wu and D. K. Yang, Reflective Liquid Crystal Displays, (John Wiley & Sons Inc., Chichester, 2005).

H. J. Coufal, D. Psaltis, and B. T. Sincerbox, eds., Holographic Data Storage, (Springer-Verlag, Berlin, 2000).

D. Goldstein, Polarized Light (Marcel Dekker, 2004).

"IEC 61947-1:2002. Electronic Projection. Measurement and documentation of key performance criteria. Part 1: Fixed resolution projectors," IEC (International Electrotechnical Commission), Geneva, 2002.

J. Campos, I. Moreno, A. Márquez, C. Iemmi, V. Mariscal, J. A. Davis, and M. J. Yzuel, "Simple Jones method for describing modulation properties of reflective liquid crystal spatial light modulators," in CP860. Information Optics: 5th International Workshop, G. Cristóbal, B. Javidi, and S. Vallmitjana, eds. (AIP, 2006), pp. 159-168.

Supplementary Material (2)

» Media 1: MOV (4085 KB)     
» Media 2: MOV (2102 KB)     

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Figures (14)

Fig. 1.
Fig. 1.

Polarization ellipse. The azimuth ψ and the ellipticity χ angles indicated in the figure have a positive value according to the sign convention explained in the text.

Fig. 2.
Fig. 2.

Degree of polarization for the 6 input SOPs.

Fig. 3.
Fig. 3.

Values for the three diattenuation components and for the total diattenuation.

Fig. 4.
Fig. 4.

Normalized Stokes parameters for the full polarized component and for the 6 input SOPs (X, Y, 45, -45, R and L), represented on the Poincaré sphere ((a), (c) and (e)), and azimuth and ellipticity representation as a function of the gray level ((b), (d) and (f)).

Fig. 5.
Fig. 5.

(a). Optical detected signal with input and output polarizers oriented at 0°, for addressed gray levels (GL) 0, 100, 200 and 250. (b). Detected signal for input polarizer oriented at 0°, 45°, 90° and 135°, with the output polarizer at 0° and for the addressed gray level 200.

Fig. 6.
Fig. 6.

Values for the elements of the Mueller matrix for the LCoS as a function of the addressed gray level.

Fig. 7.
Fig. 7.

SOP reflected by the LCoS for a linearly polarized incident SOP with 30° azimuth. (a) Representation of the DoP and the Stokes parameters as a function of the gray level; (b) Representation on the Poincaré sphere for the normalized Sokes vector (1 S n1 S n2 S n3). Symbols and continuous lines correspond to experimental and theoretical data respectively.

Fig. 8.
Fig. 8.

Maximum intensity contrast. (a). Normalized intensity (theory – line, experiment – symbols. (b). Phase-shift (experimental). Configuration given in Table 1. The low phase-shift depth enables to use this configuration for amplitude-mostly modulation.

Fig. 9.
Fig. 9.

Theoretical DoP for the SOP reflected by the LCoS. The incident SOP is (ψ 1=112°, χ 1=21°). This is the incident SOP both in Figs. 8 and 10.

Fig. 10.
Fig. 10.

Results for the PSD orthogonally oriented with respect to the PSD in Fig. 8(a) Normalized intensity (theory – line, experiment – symbols). (b) Phase-shift (experimental). The non-null at gray level 200 is mainly due to depolarized light.

Fig. 11.
Fig. 11.

Video files recorded for the interference pattern for the configuration presented in Fig. 10. The two halves of the LCoS are addressed respectively with gray levels 0 and 20 in (a) (Movie 1: 2.3 MB), and with gray levels 40 and 200 in (b) (Movie 2: 2.5 MB). [Media 1][Media 2]

Fig. 12.
Fig. 12.

Modulation in a configuration for constant intensity with only polarizers. (a). Normalized intensity (theory – line, experiment – symbols) and DoP (theory). (b). Phase-shift (experimental). Configuration given in Table 2.

Fig. 13.
Fig. 13.

Modulation in a configuration for constant intensity with elliptically polarized light. (a). Normalized intensity (theory – line, experiment – symbols). (b). Phase-shift (experimental). Configuration given in Table 2. The phase-shift depth close to 300° enables for phase-mostly modulation.

Fig. 14.
Fig. 14.

Theoretical DoP for the SOP reflected by the LCoS. In (a) for the incident SOP used in Fig. 11, and in (b) for the incident SOP used in Fig. 12.

Tables (2)

Tables Icon

Table 1. Azimuth and ellipticity angles for the SOPs generated and detected by the PSG and the PSD in the optimum modulation configurations. The orientation of the external polarization elements is also indicated.

Tables Icon

Table 2. Azimuth and ellipticity angles for the SOPs generated and detected by the PSG and the PSD in the optimum modulation configurations. The orientation of the external polarization elements is also indicated.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

( S 0 S 1 S 2 S 3 ) = ( I 0 I x I y I 45 I 45 I R I L )
DoP = S 1 2 + S 2 2 + S 3 2 S 0
D X = S 0 X S 0 Y S 0 X + S 0 Y , D 45 = S 0 45 S 0 45 S 0 45 + S 0 45 , D c = S 0 R S 0 L S 0 R + S 0 L
D = S 0 max S 0 min S 0 max + S 0 min
D = D X 2 + D 45 2 + D C 2
S n 1 , n 2 , n 3 = S 1 , 2 , 3 I pol ,
I pol = S 1 2 + S 2 2 + S 3 2

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